what does the "compton effect" tell us?
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Compton
Although Max Planck and Albert Einstein postulated that light could behave as both a wave and a particle, it was Arthur Compton who finally proved that this was possible. His experiment involved scattering photons off electrons and offered proof for what we now refer to as the Compton effect.
The compton effect (also known as compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule.
The Compton effect was observed by Arthur Compton in 1922, by observing the "scattering of x-rays from electrons in a carbon target, and finding scattered x-rays with a longer wavelength than those incident upon the target. The shift of the wavelength increased with scattering angle according to the Compton formula:
Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength according to Planck’s relationship" [8].
By that time the photoelectric effect suggested that light consisted of particles was really debated.
The compton's original experiment made use of molybdenum K-alpha x-rays, which have a wavelength of 0.0709 nm. These were scattered from a block of carbon and observed at different angles with a Bragg spectrometer. The spectrometer consists of a rotating framework with a calcite crystal to diffract the x-rays and an ionization chamber for detection of the x-rays. Since the spacing of the crystal planes in calcite is known, the angle of diffraction gives an accurate measure of the wavelength.
Figure 1. Compot Experiment.
By Compton observation, after the scattering the frequency (energy) of the x-rays had changed, and had always decreased. From the point of view of classical (wave) electromagnetic theory, this frequency shift cannot be explained since the frequency is a property of the incoming electromagnetic wave and cannot be altered by the change of direction implied by the scattering.
If, on the other hand, the incoming radiation is thought of as a beam of photons (electromagnetic quanta) then the situation becomes that of photons of energy
E = hv.
scattering from free electrons in the target material. Energy-momentum conservation, applied to this situation, predicts that the scattered photons will have an energy of:
E' = hv' <E.
in complete agreement with Compton’s experiments.
The frequency shift will depend on the angle of scattering, and can be calculated from kinematics. Consider an incoming photon of energy hv and momentum hv/c scattering from any electron of mass m. p is the momentum of the electron after scattering and hv', hv'/c are the energy and momentum of the scattered photon.
For momentum conservation, the three vectors hv/c, hv'/c and p must lie in the same plane.
Figure 2. Compton scattering diagram showing the relationship of the incident photon and electron initially at rest to the scattered photon and electron given kinetic energy.
This what actually led to the compton formula.
" Compton and his coworkers realized the classical wave theory of light failed to explain the scattering of X-rays from electrons. According to classical mechanics, electromagnetic waves of frequency f0, incident on electron should have two effects:
Radiation pressure should cause acceleration of electrons in the direction of the radiation.
The oscillating field of X-ray should set electrons in oscillation at frequency f`, where f`is the frequency in the frame of the moving electron.
The apparent frequency f`of the electron is different than f0 because of the Doppler’s effect. Each electron first absorbs radiation as a moving particle and then reradiates as a moving particle, thereby exhibiting two Doppler shifts in the frequency of radiation. Because different electrons move at different speeds after the interaction, depending on the amount of energy absorbed from the incident electromagnetic waves, scattered wave frequency should show a distribution of Doppler shifted value in relation to angle of approach." [3].
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect.
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